"The laws of nature are but the mathematical thoughts of God"

- Euclid

Mathematics is everywhere in this universe. We seldom note it. We enjoy nature and are not interested in going deep about what mathematical idea is in it. Here are a very few properties of mathematics that are depicted in nature.

**SYMMETRY**

*Symmetry is when a figure has two sides that are mirror images of one another. It would then be possible to draw a line through a picture of the object and along either side the image would look exactly the same. This line would be called a line of symmetry.*

**There are two kinds of symmetry.**

One is

**bilateral symmetry**in which an object has two sides that are mirror images of each other.

*The human body would be an excellent example of a living being that has bilateral symmetry.*

**.**

*Few more pictures in nature showing bilateral symmetry*The other kind of symmetry is

**radial symmetry.**This is where there is a center point and numerous lines of symmetry could be drawn.

*The most obvious geometric example would be a circle.*

*Few more pictures in nature showing radial symmetry.***SHAPES**

**Sphere:**

*A sphere is a perfectly round geometrical object in three-dimensional space, such as the shape of a round ball.*

The shape of the Earth is very close to that of an oblate spheroid, a sphere flattened along the axis from pole to pole such that there is a bulge around the equator.

**Hexagons:**

*Hexagons are six-sided polygons, closed, 2-dimensional, many-sided figures with straight edges.*

For a beehive, close packing is important to maximise the use of space. Hexagons fit most closely together without any gaps; so hexagonal wax cells are what bees create to store their eggs and larvae.

**Cones:**

*A cone is a three-dimensional geometric shape that tapers smoothly from a flat, usually circular base to a point called the apex or vertex.*

Volcanoes form cones, the steepness and height of which depends on the runniness (viscosity) of the lava. Fast, runny lava forms flatter cones; thick, viscous lava forms steep-sided cones.

**Few more cones in nature:**

**Parallel lines:**

*In mathematics, parallel lines stretch to infinity, neither converging nor diverging.*

These parallel dunes in the Australian desert aren't perfect - the physical world rarely is.

**Fibonacci spiral:**

*If you construct a series of squares with lengths equal to the Fibonacci numbers (1,1,2,3,5, etc) and trace a line through the diagonals of each square, it forms a Fibonacci spiral*.

Many examples of the Fibonacci spiral can be seen in nature, including in the chambers of a nautilus shell.